Do you mind if I offer a critique? There are a few minor points that could be improved.
in reply to Re^3: Generate the perl sequence 1, 11, 111, ....
in thread Generate the perl sequence 1, 11, 111, ....
If all that $one_literal can contain is "1", then the variable isn't needed.
If $one_literal can contain something other than "1", then it's misnamed.
Speaking of being misnamed, $one_literal doesn't contain a literal. It contains a string. String literals are pieces of source code that get compiled into strings. They don't exist anywhere but in source code.
The first argument of printf is a formatting string. Using it to print arbitrary string is a trap waiting to be sprung. Instead, use print or printf('%s', ...).
The C syntax for "for" loops (for ( my $i = 1; $i <= $counter; $i++ )) is much more complex than alternative syntax Perl provides (for my $i ( 1..$counter )). That makes it more error-prone and harder to parse mentally (small variations will be obscured).